.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/elements/solid187/example_solid187.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_elements_solid187_example_solid187.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_elements_solid187_example_solid187.py:


.. _ref_solid187_example:

TET10 — prescribed uniform strain on a 10-node tet
=====================================================

Single TET10 (10-node quadratic tet) driven by a fully-prescribed
displacement field that matches a uniform strain state. Under
all-Dirichlet BCs the solve has a unique solution equal to the
prescribed field, so the recovered strain tensor matches the analytical
one to machine precision. Useful as a self-contained smoke test that
``TET10`` + :meth:`femorph_solver.Model.eel` are in lockstep.

.. GENERATED FROM PYTHON SOURCE LINES 14-24

.. code-block:: Python


    from __future__ import annotations

    import numpy as np
    import pyvista as pv
    from vtkmodules.util.vtkConstants import VTK_QUADRATIC_TETRA

    import femorph_solver
    from femorph_solver import ELEMENTS








.. GENERATED FROM PYTHON SOURCE LINES 25-29

Reference 10-node unit tet
--------------------------
Corners at (0,0,0), (1,0,0), (0,1,0), (0,0,1); mid-edge nodes in
VTK_QUADRATIC_TETRA order halfway along each edge.

.. GENERATED FROM PYTHON SOURCE LINES 29-54

.. code-block:: Python

    E = 2.1e11  # Pa
    NU = 0.30
    EPS_XX = 5.0e-4
    EPS_YY = -NU * EPS_XX  # Poisson contraction

    I = np.array([0.0, 0.0, 0.0])
    J = np.array([1.0, 0.0, 0.0])
    K = np.array([0.0, 1.0, 0.0])
    L = np.array([0.0, 0.0, 1.0])
    coords = np.array(
        [
            I,
            J,
            K,
            L,
            0.5 * (I + J),  # 5
            0.5 * (J + K),  # 6
            0.5 * (K + I),  # 7
            0.5 * (I + L),  # 8
            0.5 * (J + L),  # 9
            0.5 * (K + L),  # 10
        ],
        dtype=np.float64,
    )








.. GENERATED FROM PYTHON SOURCE LINES 55-58

Build the model + prescribed displacement
-----------------------------------------
Apply ``u = (εxx·x, εyy·y, εyy·z)`` at every node.

.. GENERATED FROM PYTHON SOURCE LINES 58-70

.. code-block:: Python

    cells = np.concatenate([[10], np.arange(10, dtype=np.int64)])
    cell_types = np.array([VTK_QUADRATIC_TETRA], dtype=np.uint8)
    grid = pv.UnstructuredGrid(cells, cell_types, coords)

    m = femorph_solver.Model.from_grid(grid)
    m.assign(ELEMENTS.TET10, material={"EX": E, "PRXY": NU})

    for i, (x, y, z) in enumerate(coords, start=1):
        m.fix(nodes=[i], dof="UX", value=EPS_XX * x)
        m.fix(nodes=[i], dof="UY", value=EPS_YY * y)
        m.fix(nodes=[i], dof="UZ", value=EPS_YY * z)








.. GENERATED FROM PYTHON SOURCE LINES 71-73

Solve + verify strain recovery
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 73-82

.. code-block:: Python

    res = m.solve()
    eps = m.eel(res.displacement)

    print(f"εxx prescribed = {EPS_XX:.3e}  |  recovered (mean) = {eps[:, 0].mean():.3e}")
    print(f"εyy prescribed = {EPS_YY:.3e}  |  recovered (mean) = {eps[:, 1].mean():.3e}")
    np.testing.assert_allclose(eps[:, 0], EPS_XX, rtol=1e-10)
    np.testing.assert_allclose(eps[:, 1], EPS_YY, rtol=1e-10)
    np.testing.assert_allclose(eps[:, 2], EPS_YY, rtol=1e-10)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    εxx prescribed = 5.000e-04  |  recovered (mean) = 5.000e-04
    εyy prescribed = -1.500e-04  |  recovered (mean) = -1.500e-04




.. GENERATED FROM PYTHON SOURCE LINES 83-85

Render the deformed tet coloured by εxx
---------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 85-103

.. code-block:: Python

    grid = femorph_solver.io.static_result_to_grid(m, res)
    node_nums = m.node_numbers
    node_to_idx = {int(nn): i for i, nn in enumerate(node_nums)}
    grid.point_data["eps_xx"] = np.array(
        [eps[node_to_idx[int(nn)], 0] for nn in grid.point_data["ansys_node_num"]]
    )

    plotter = pv.Plotter(off_screen=True)
    plotter.add_mesh(grid, style="wireframe", color="gray", line_width=1, opacity=0.4)
    plotter.add_mesh(
        grid.warp_by_vector("displacement", factor=200.0),
        scalars="eps_xx",
        show_edges=True,
        cmap="viridis",
        scalar_bar_args={"title": "εxx"},
    )
    plotter.add_axes()
    plotter.show()



.. image-sg:: /gallery/elements/solid187/images/sphx_glr_example_solid187_001.png
   :alt: example solid187
   :srcset: /gallery/elements/solid187/images/sphx_glr_example_solid187_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.232 seconds)


.. _sphx_glr_download_gallery_elements_solid187_example_solid187.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: example_solid187.ipynb <example_solid187.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: example_solid187.py <example_solid187.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: example_solid187.zip <example_solid187.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_